Size-structured populations: immigration, (bi)stability and the net growth rate

We consider a class of physiologically structured population models, a first order nonlinear partial differential equation equipped with a nonlocal boundary condition, with a constant external inflow of individuals. We prove that the linearised system is governed by a quasicontraction semigroup. We also establish that linear stability of equilibrium solutions is governed by a generalized net reproduction function. In a special case of the model ingredients we discuss the nonlinear dynamics of the system when the spectral bound of the linearised operator equals zero, i.e. when linearisation does not decide stability. This allows us to demonstrate, through a concrete example, how immigration might be beneficial to the population. In particular, we show that from a nonlinearly unstable positive equilibrium a linearly stable and unstable pair of equilibria bifurcates. In fact, the linearised system exhibits bistability, for a certain range of values of the external inflow, induced potentially by All\'{e}e-effect.Comment: to appear in Journal of Applied Mathematics and Computin

Syzygies of torsion bundles and the geometry of the level l modular variety over M_g

We formulate, and in some cases prove, three statements concerning the purity or, more generally the naturality of the resolution of various rings one can attach to a generic curve of genus g and a torsion point of order l in its Jacobian. These statements can be viewed an analogues of Green's Conjecture and we verify them computationally for bounded genus. We then compute the cohomology class of the corresponding non-vanishing locus in the moduli space R_{g,l} of twisted level l curves of genus g and use this to derive results about the birational geometry of R_{g, l}. For instance, we prove that R_{g,3} is a variety of general type when g>11 and the Kodaira dimension of R_{11,3} is greater than or equal to 19. In the last section we explain probabilistically the unexpected failure of the Prym-Green conjecture in genus 8 and level 2.Comment: 35 pages, appeared in Invent Math. We correct an inaccuracy in the statement of Prop 2.

Unanticipated differences between α- and γ-diaminobutyric acid-linked hairpin polyamide-alkylator conjugates

Hairpin polyamide–chlorambucil conjugates containing an {alpha}-diaminobutyric acid ({alpha}-DABA) turn moiety are compared to their constitutional isomers containing the well-characterized {gamma}-DABA turn. Although the DNA-binding properties of unconjugated polyamides are similar, the {alpha}-DABA conjugates display increased alkylation specificity and decreased rate of reaction. Treatment of a human colon carcinoma cell line with {alpha}-DABA versus {gamma}-DABA hairpin conjugates shows only slight differences in toxicities while producing similar effects on cell morphology and G2/M stage cell cycle arrest. However, striking differences in animal toxicity between the two classes are observed. Although mice treated with an {alpha}-DABA hairpin polyamide do not differ significantly from control mice, the analogous {gamma}-DABA hairpin is lethal. This dramatic difference from a subtle structural change would not have been predicted

Heat storage in alloy transformations

The feasibility of using metal alloys as thermal energy storage media was determined. The following major elements were studied: (1) identification of congruently transforming alloys and thermochemical property measurements; (2) development of a precise and convenient method for measuring volume change during phase transformation and thermal expansion coefficients; (3) development of a numerical modeling routine for calculating heat flow in cylindrical heat exchangers containing phase change materials; and (4) identification of materials that could be used to contain the metal alloys. Several eutectic alloys and ternary intermetallic phases were determined. A method employing X-ray absorption techniques was developed to determine the coefficients of thermal expansion of both the solid and liquid phases and the volume change during phase transformation from data obtained during one continuous experimental test. The method and apparatus are discussed and the experimental results are presented. The development of the numerical modeling method is presented and results are discussed for both salt and metal alloy phase change media

Cosmology, cohomology, and compactification

Ashtekar and Samuel have shown that Bianchi cosmological models with compact spatial sections must be of Bianchi class A. Motivated by general results on the symmetry reduction of variational principles, we show how to extend the Ashtekar-Samuel results to the setting of weakly locally homogeneous spaces as defined, e.g., by Singer and Thurston. In particular, it is shown that any m-dimensional homogeneous space G/K admitting a G-invariant volume form will allow a compact discrete quotient only if the Lie algebra cohomology of G relative to K is non-vanishing at degree m.Comment: 6 pages, LaTe

The Vacuum Structure and Spectrum of N=2 Supersymmetric SU(N) Gauge Theory

We present an exact description of the metric on the moduli space of vacua and the spectrum of massive states for four dimensional N=2 supersymmetric SU(n) gauge theories. The moduli space of quantum vacua is identified with the moduli space of a special set of genus n-1 hyperelliptic Riemann surfaces.Comment: 11 pages, Revtex, 2 figures. Reference adde

DNA uptake into nuclei: Numerical and analytical results

The dynamics of polymer translocation through a pore has been the subject of recent theoretical and experimental works. We have considered theoretical estimates and performed computer simulations to understand the mechanism of DNA uptake into the cell nucleus, a phenomenon experimentally investigated by attaching a small bead to the free end of the double helix and pulling this bead with the help of an optical trap. The experiments show that the uptake is monotonous and slows down when the remaining DNA segment becomes very short. Numerical and analytical studies of the entropic repulsion between the DNA filament and the membrane wall suggest a new interpretation of the experimental observations. Our results indicate that the repulsion monotonically decreases as the uptake progresses. Thus, the DNA is pulled in (i) either by a small force of unknown origin, and then the slowing down can be interpreted only statistically; (ii) or by a strong but slow ratchet mechanism, which would naturally explain the observed monotonicity, but then the slowing down requires additional explanations. Only further experiments can unambiguously distinguish between these two mechanisms.Comment: 12 pages, 6 figures, submitted to J. Phys. Cond. Ma

Recording, analysis, and interpretation of spreading depolarizations in neurointensive care: Review and recommendations of the COSBID research group.

Spreading depolarizations (SD) are waves of abrupt, near-complete breakdown of neuronal transmembrane ion gradients, are the largest possible pathophysiologic disruption of viable cerebral gray matter, and are a crucial mechanism of lesion development. Spreading depolarizations are increasingly recorded during multimodal neuromonitoring in neurocritical care as a causal biomarker providing a diagnostic summary measure of metabolic failure and excitotoxic injury. Focal ischemia causes spreading depolarization within minutes. Further spreading depolarizations arise for hours to days due to energy supply-demand mismatch in viable tissue. Spreading depolarizations exacerbate neuronal injury through prolonged ionic breakdown and spreading depolarization-related hypoperfusion (spreading ischemia). Local duration of the depolarization indicates local tissue energy status and risk of injury. Regional electrocorticographic monitoring affords even remote detection of injury because spreading depolarizations propagate widely from ischemic or metabolically stressed zones; characteristic patterns, including temporal clusters of spreading depolarizations and persistent depression of spontaneous cortical activity, can be recognized and quantified. Here, we describe the experimental basis for interpreting these patterns and illustrate their translation to human disease. We further provide consensus recommendations for electrocorticographic methods to record, classify, and score spreading depolarizations and associated spreading depressions. These methods offer distinct advantages over other neuromonitoring modalities and allow for future refinement through less invasive and more automated approaches

“Clip-Stone” Filiation Within the Biliary Tract

A case of cholangitis due to the migration of a metal clip used for surgical cholecystectomy 4 years earlier, is reported. The diagnostic approach and therapeutic options, either endoscopic or surgical are discussed. The use of resorbable clips during the performance of laparoscopic cholecystectomy should avoid this type of complication